2004 AIME I Problems/Problem 13
The polynomial has 34 complex roots of the form with and Given that where and are relatively prime positive integers, find
This expression has roots at every 17th root and 19th root of unity, other than 1. Since 17 and 19 are relatively prime, this means there are no duplicate roots. Thus, and are the five smallest fractions of the form or for .
and can both be seen to be larger than any of , so these latter five are the numbers we want to add.
and so the answer is .